{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to Quantitative Finance\n",
    "\n",
    "Copyright (c) 2019 Python Charmers Pty Ltd, Australia, <https://pythoncharmers.com>. All rights reserved.\n",
    "\n",
    "<img src=\"img/python_charmers_logo.png\" width=\"300\" alt=\"Python Charmers Logo\">\n",
    "\n",
    "Published under the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) license. See `LICENSE.md` for details.\n",
    "\n",
    "Sponsored by Tibra Global Services, <https://tibra.com>\n",
    "\n",
    "<img src=\"img/tibra_logo.png\" width=\"300\" alt=\"Tibra Logo\">\n",
    "\n",
    "\n",
    "## Module 1.6: Time Series\n",
    "\n",
    "### 1.6.3 White Noise\n",
    "\n",
    "In short, a time series is white noise if it is random and unpredictable.\n",
    "\n",
    "As with most mathematical terms, it is more formally defined. A time series $X$ is white noise if it:\n",
    "\n",
    "* has a mean of zero, that is $E[X] = 0$\n",
    "* the variance is constant over time\n",
    "* There is no correlation within the data at different lag periods: $E[X_t X_{t-k}] = 0$ when $k \\neq 0$\n",
    "\n",
    "To test formally if \"variance is constant over time\":\n",
    "\n",
    "Let $\\gamma_k = E[(X_t - \\mu)(X_{t-k} - \\mu)]$\n",
    "\n",
    "$\\rho_k = \\frac{\\gamma_k}{\\gamma_0}$\n",
    "\n",
    "The data is stationary if $\\rho_k \\rightarrow 0$ as $k \\rightarrow \\infty$, and it is white noise if also     $\\frac{\\rho_k}{m} \\sim N(0, 1)$, where $m= \\sqrt{\\frac{1}{n}}$\n",
    "\n",
    "Additionally the term *independent white noise* is also used when the variables in multivariable model are independent and have no correlation. Note that some require this as part of the test for \"white noise\" itself, but it is normally considered a stronger assumption than normally for \"white noise\".\n",
    "\n",
    "Let's have a look at the most random of data series, and what type of statistics we can glean to see if it is white noise:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%run setup.ipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "distribution = norm(0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(100)  # For consistent results. Remove this line to get random results\n",
    "X = distribution.rvs(3000)  # Random data, between 0 and 1, then with 0.5 subtracted\n",
    "# Note we are considering this as a \"time series\" data, so X[1] happens after X[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1d3219aa1d0>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiIAAAGdCAYAAAAvwBgXAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy88F64QAAAACXBIWXMAAA9hAAAPYQGoP6dpAAB1Y0lEQVR4nO2dfZRfRXn4n28W84LJbtjNEpLdhaBypAr2WCkaNK0cqC8FTY1pESMC+tODJJpV2PIWCftrEWrVxdqWqq1YT0jihg3aerT8CGwQj4CoQQERrQZIQgCFkkSRld3M74/b2dy9OzP3eWaeuS/f7/M5Z84mu9/vvXPnzsszz9s0lFIKBEEQBEEQSmBG2RUQBEEQBKF1EUFEEARBEITSEEFEEARBEITSEEFEEARBEITSEEFEEARBEITSEEFEEARBEITSEEFEEARBEITSEEFEEARBEITSOKzsCrg4ePAgPP744zBv3jxoNBplV0cQBEEQBARKKThw4AAsXrwYZsxw6zwqLYg8/vjj0NfXV3Y1BEEQBEHwYNeuXdDb2+v8TKUFkXnz5gFA8iDt7e0l10YQBEEQBAz79++Hvr6+yXXcRaUFEW2OaW9vF0FEEARBEGoGxq1CnFUFQRAEQSgNEUQEQRAEQSgNEUQEQRAEQSiNwgSRa6+9FhqNBvT39xd1S0EQBEEQKk4hgsi9994Ln//85+FVr3pVEbcTBEEQBKEmRBdEfvOb38CqVavgi1/8IhxxxBGxbycIgiAIQo2ILoisXr0azjjjDDj99NNzPzs2Ngb79++fUgRBEARBaF6i5hHZvHkz/PCHP4R7770X9flrrrkGBgcHY1ZJEARBEIQKEU0jsmvXLli7di3ceOONMHv2bNR3LrvsMti3b99k2bVrV6zqCYJQESYmALZvB9i0Kfk5MVF2jQRBKJKGUkrFuPDXvvY1eMc73gFtbW2Tv5uYmIBGowEzZsyAsbGxKX8zsX//fujo6IB9+/ZJZlVBaEK2bgVYuxZg9+5Dv+vtBfjsZwFWrCivXoIghEFZv6OZZk477TS4//77p/zu/PPPh+OPPx4uueSSXCFEEITmZutWgJUrAbJboT17kt/fdJMII4LQCkQTRObNmwcnnHDClN+9+MUvhq6urmm/FwShtZiYSDQhJn2sUgCNBkB/P8Dy5QCyZxGE5kYyqwqCUDh33jnVHJNFKYBdu5LPCYLQ3BR6+u727duLvJ0gCBVl717ezwmCUF9EIyIIQuEsWsT7OUEQ6osIIoIgFM6yZUl0TKNh/nujAdDXl3xOEITmRgQRQRAKp60tCdEFmC6M6P9fd504qgpCKyCCiCAIpbBiRRKi29Mz9fe9vRK6KwitRKHOqoIgCGlWrEhCdO+8M3FMXbQoMceIJkQQWgcRRARBKJW2NoA3vrHsWgiCUBZimhEEQRAEoTREEBEEQRAEoTREEBEEQRAEoTREEBEEQRAEoTREEBEEQRAEoTREEBEEQRAEoTREEBEEQRAEoTQkj4hQOhMTktBKEAShVRFBRCiVrVsB1q4F2L370O96e5NzSCTFtyAIQvMjphmhNLZuBVi5cqoQAgCwZ0/y+61by6mXIAiCUBwiiAilMDGRaEKUmv43/bv+/uRzgiAIQvMigohQCnfeOV0TkkYpgF27ks8JgiAIzYsIIkIp7N3L+zlBEAShnoizqlAKixbxfo4bieQRBEEoBtGICKWwbFkSHdNomP/eaAD09SWfK5qtWwGWLAE49VSAd787+blkiTjPCoIgxEAEEaEU2tqSEF2A6cKI/v911xWvhZBIHkEQhGIRQUQojRUrAG66CaCnZ+rve3uT3xedR0QieQRBEIpHfESEUlmxAmD58mr4Y1Aied74xsKqJQiC0NSIICKUTltbNRZ2ieQRBEEoHjHNCML/UvVIHkEQhGZEBBFB+F+qHMkjCILQrIggIgj/SzqSJ0uZkTyCIAjNjAgigpChs9P8uzIieQRBEJodcVYVhP9F5xAxhe8+/XTx9REEQWgFRCMiCODOIQKQmGYkh4ggCAI/IogIAshpwIIgCGUhphlBAMkhUjZyyKAgtC4iiAgCSA6RMtm6NTGLpTVSvb1JBJM4BwtC8yOmGUEAySFSFnLIoCAIIogIAlT3NOBmRg4ZFAQBILIgcv3118OrXvUqaG9vh/b2dli6dCl861vfinlLQfCmaqcBNzviICwIAkBkH5He3l649tpr4bjjjgOlFPz7v/87LF++HHbs2AGvfOUrY95aELyo0mnAzY44CAuCABBZEHnb29425f9XX301XH/99XD33XeLICJUlqqcBtzsiIOwIAgABUbNTExMwJYtW+C3v/0tLF261PiZsbExGBsbm/z//v37i6qeIAgFox2E9+wx+4k0GsnfxUFYEJqb6M6q999/P8ydOxdmzZoFF1xwAdx8883wile8wvjZa665Bjo6OiZLX19f7OoJglAS4iAsCAIAQEMpW1JrHn7/+9/DY489Bvv27YObbroJ/vVf/xXuuOMOozBi0oj09fXBvn37oL29PWY1BUEoCVMekb6+RAgRB2EhJiGJ9CQJn5v9+/dDR0cHav2OLohkOf300+GlL30pfP7zn8/9LOVBBEGoLzKpC0UTkkhPkvDlQ1m/C8+sevDgwSlaD0EQBHEQForEdtK2TqTnCtcP+a5gJqqPyGWXXQbf/va34ZFHHoH7778fLrvsMti+fTusWrUq5m0FQRAEwUhIIj1JwheHqILIU089Be9973vh5S9/OZx22mlw7733wi233AJ/9md/FvO2giAIgmAkJJGeJOGLQ1TTzL/927/FvLwgCIIgkAhJpCdJ+OIgp+8KQkURB05B4CckkZ4k4YuDHHonCBVk61aAJUsATj0V4N3vTn4uWSKn0QpCKCEnbcsp3XEQQURoKSYmALZvB9i0KfkZw6ks9B7aKz9ri9Ze+SKMCII/IYn0JAlfHEQQEVqGIrQMofcQr3xBiE/ISdtySjc/hSc0oyAJzQQubLH/ehfDMYFw3GP79kR4yWN0VPJuCEIoklk1HpXOrEpBBBGBg4mJRCthC7vTh6vt3Ok/kXDdY9OmRJOSx8aNAGef7VVVoabIwifUCcr6LaYZoekpIvaf6x7ilS+YEOdloZkRQURoeoqI/ee6h3jlC1nEeVlodkQQEZqeIrQMXPcQr3whTZnOy0VEmAkCgAgiQgtQhJaB8x7ilS9oykopLqYgoUhEEBGaAtfurQgtA/c9VqwAeOSRJDpm48bk586dIoS0GmWkFBdTUFxE0zQdEUSE2oPZvRWhZeC+R1tbEqJ79tnJTzHHtB5FOy9LHpu4iKbJjITvCrWGmrujiBBICbMUuNBh4Xv2mIUDjtDzNJLHJh5F5DKqEpT1Ww69E2pL3u6t0Uh2b8uXH5qktZYhJkXcQ2gNtMlv5cqkP6f7egznZTldNg4+c1UrIaYZobaU5cgnCEVSpPOy5LGJg8xVbkQjItQW2b0JrcKKFcluObbJT0d/5ZmCJI8NDZmr3IggItQW2b0JrURRZsUiTUGtgsxVbsQ0I9QWyULaulQ9BLLq9XMheWz4kbnKjQgiQm2RLKStSdVDIKtePwySx4YXmavcSPiuUHu2bk080tPOYH19ycCWibO5qHoIZNXrJ5RLK81VlPVbBBGhKZDcHc2Pzqlhiz7gzqlBper1E6pBq8xVkkdEaDkkd0fzQwmBLKMvVL1+QjWQuWo6Ioi0OHWXzutefwFP1UMgq16/IihjPMocUH9EEGlhTPbK3t7EqaoO9sq611+gUfUQyKrXLzZljEeZA5oD8RFpUeruVFf3+gt0ij53hUrV6xeTMsajzAHVRpxVBSd1d6qre/0Ff/TiA2BOtlX24lP1+sWgjPEoc0D1oazfkkekBan7uQd1r7/gT9WTbVW9fjEoYzzKHNBciI9IC1J3p7q6118Ig+PclZgOjkWdC1MVyhiPMgc0FyKItCB1d6qre/2FhBBhICQEsggHx1YK0SxjPMoc0FyIj0gLUnenurrXXygv2kEcHPkpYzzKHFB9xEdEcFL3cw+qXv86H3hWBFoYyNr49+xJfh/rTJaJiUT4MS1c+nf9/fK+qJQxHqs2B8iYD0RVmH379ikAUPv27Su7Kk3JyIhSvb1KJdNwUvr6kt/XgSrW31Sn3t76tGlsxsent0+6NBrJOxwf57/36Kj9vukyOsp/71agjPFYhTlAxrwZyvotppkWRdvn9+wB+NWvALq7E0//UKe6orMcVimroqj989m+PTmNNo/RUX4fi02bktNw89i4EeDss3nv3Sq0WmZVGfN25KwZwYnLPh8ygMuw+1fFKTBP7d9oJGr/5cura/IqgjKjHTgdHKskAFeJMsZjWXOAjHk+xEekJGLYFDHXjGWfL8vuXxUkrwGOMqMdli1LBOOsT4Gm0UiOZF+2zH2drVsTR8lTT000LKeemvy/2fu4MBUZ83yIIFICMSYyzDVjOevVyQkwllOZ5DXAwSUM+MDh4NjqArdwCBnzfIggUjAxJjLsNTkkeNNCXpedQcydrOQ1wFF2tENI5tM6CdwCL6Z5T8Y8IzG9Zj/xiU+ok046Sc2dO1d1d3er5cuXq5/+9Kfo7zdb1EyMiAHKNTduxEUNbNxovpfNO7y/P+y6RTAykrSFqX0ajXAPd/0eTPeIHQ1SR8qOdhgfT6JjNm5MfmLei0TdtCa2eW94WMa8C8r6HVUjcscdd8Dq1avh7rvvhltvvRVeeOEFeNOb3gS//e1vY962ssTQHFCuSZXg07uA//t/7VqX666jXbdoitjJlr3TrxsrVgA88kgSHbNxY/Jz587iIgy0g+PZZyc/Me+ljqp4yW8RhkvbfNZZh6KrZMwHUoBgNMlTTz2lAEDdcccdqM83m0YkVCMRek3Krt20C3CVtrbq7gyK3MmWvdMX4lE3jYjktwgDq23essV/zPto5uoCZf0uNHx33759AADQ2dlp/PvY2BiMjY1N/n///v2F1KsoYtgUKdfUu/aVKxOJPa0hSEvwX/+6OTbehd5pua5b1s6gyJ1sqx141kpoR9u8tOIxHG2p2PJbaL+xVs5vgQWrbV6wINHuUcd8EekOahNmXoBgpJRSamJiQp1xxhnq9a9/vfUz69evVwAwrTSLRiSGH4HPNV279rxdgKv091dTG1C3naxQXbSvUXa8cfkacVBm9tpmIoYGWxPbZ03fo0yNGEUjUpggcsEFF6hjjjlG7dq1y/qZ559/Xu3bt2+y7Nq1q6kEEaXwExlFZeczOdquj120bQt5FVWN4kgqcFJ18xt2DA8NSZ93EWsDU4SgWISgk0flBJHVq1er3t5e9ctf/pL0vWbzEdHkTWQ+kizX5IjdBdRtIecU1gShSn0jW5cNG/BjV3xG7MTawMTW0FZFI1YZQeTgwYNq9erVavHixepnP/sZ+fvNKogoZZ/IbJKsLq5Jg2NypGpEqqSSzoMirJWt1hSqQZUEDhOmfrpgQXOO3zKIYYqLafJRqjqm6MoIIh/60IdUR0eH2r59u9q7d+9kee6551Dfb2ZBxATGP6OrK+5kmLcLyJYqqaQxYBaWKqg1hfKpujCat2mhCCNV12iWCbcpLragEFvQwVKZ03cbljzON9xwA5x33nm532+103exJ5MODgJceWW8emiPe4Cky2p0RMzgIMBxx033wq6Nh7aDiYkk26rNW15HRuzcWb9nE/BU/VTVvH6qyUaxuYhx4nGzwDm36XeXF33lO8eUecJ1GtL6HVcmCqPVNCJYSTa2VkQp+i6g6rtHLFVRawoJZZhGqmJjd4Htp93deM1ImZmP60hI34wZfVUV5/zKZFYVaGBzgjz9dPxzWyiZL5vpILA6Zs9sVso65ZaaAbmM7KXY/jc0lBQMciYKntC+GXLmUR61zPIcVyYKo9U0IuPjSnV21mv3UofdIwXRiFSDMv10KDb2sjSBlH5alR1ys8DZN2Nq/Gx9c3CwGA1jZZxVQ2k1QUSppJOUtRDKQWAyaVeBsoVbbJ8eHCxPWKL20zokYqsDZfdNKuk5fXCwWKFZTDM15oorALq67H9vNAD6+vjTSPuqGpvNlOFSawIkw/f//J9i69RqxDgckoJO5W7xtZ90JvziF5O6mOoHEH6Qoguq+j2mKaCVKLtvUtGHO86aBXDVVdU1n4sgUjHa2gC+8AXzJBjLvhfi4xF6fk4VTwe1Tdqa9euL8VVoBUzvv2zhFrPIf+AD5S9IVOGi7BOPm4Ey+mboHFnE6ePBxFHK8NCKphlNUWmkQ1WNIaaMqkfajI/bTWWi0g7HZcOugrnPNQapuRpi+gJUPelaM1G0KZpjjizLfC4+IgxUYXAXUQeOTupjf65D0rC62YOxVKFvu94/QBKiXgU/ndAzmUZHqy9wC3iK9CHjmiPLSnAmgkggdZs4QhYWrk5K0eDUYYEfH08OBStjJxGTKvRtzPvXgkhVnSuxC9KWLdUXuG1UQWCtIpiNV2jbcc6RohEJpAxBpA479TShCwtnJ80OvrGx8N1kGZjatMidRCyq0rcpUSlVPuU2b0EaHq6+wG2jCgJrlXFtvKpmTikrElAEEU/qsFNPw7GwxOqkrsFYlbMQlJouPNl2sFUUmChUqW9T3n/Vd+W2BWl4uDiNGncbVUVgrTqmdq+qOaWM8G0RRDyp+k49DefCwt1J8wZjlZ0R29poQkhbWyK8VJmqmZlCxlkVBROTMFuURo1bc1ElgbVucLVdrPFaVACERgQRT6q0U8+DW2ji6qSYwdjbG6aFwS5Grs9xnVyq61vVXWIVzUy+Wrg6mAtGRuj9x1f4i6G5qNNmrGpwOf5jxquvQFikIC+CiCd1GoQxhCaOTkrNSknVwmAXI9fn8oQlH0GEMikUNRls2VLcokiFqoWrg7lgfDxxso3Vb7L3iqG5qNNmrGqEth12c4Tt82VrD0UQ8WRsLF8139aWfM5EkS++qkJT6DkdeSf8YhYjLtNQjEW8qF398DDNzFSGyh37/utiLti2jdbeIQJUrPFfFbNpVXHN8aEmR+zmCKOproL2UAQRT0I6UtEvvqpnolDbkGJmyRuovb2JkJi3aGEPFqQWTIhzEbt6qnmgTK0C5v3HWHQpmwbsZ9etw7d5qG0+lka0pyf/mr295Qt9ZZA3x4fMydg+PjSU3/ZV0R6KIOKJ7+Au68VX8SCrWAISdqCed14cISN0ISxqV+9jdqpSSKyJGBEE2E0D5bNYQeQ97wl/zzGEM4pZtdWgamOpczJXH6+S9lAEEU98BnfZL75oT2hsnbgFJOxAxZbOTrc9NmvWcJk5MO+4KFMa9j66YHZYZcPZdpRNA3WDgTXNbNsW3iYxBH7xDzFDneN95mSuPl4lk70IIp74DO4qvPiynZJMmAZjd7dS/f1+daQusHklz1l2eNicX8RXuCpqkqcIbFXwq8DAtehSFhSfDQbGWbWri6/NuQX+KsxlVcR3g0qZk7n6eJWESRFEArAN7vQClu4MVXrxVUMPxv7+RAhJtwfVf4Yr0iU9oH2cZX21T1XUiAwPh91LU4QgnDcuOd/Btm3+7yvPP4dbU8mpEa2q31kMKH22qDmeQ7CskjApgkggebHc6UW0Si++inD6z/g4Yebdk5qTZMOGxJyxYQNt0S1qks+7j60f+1Kkk/bIiFnj0NWFux92QensTIRn38VnZGS602dsx3UuQbBMvzNugdZ2PWqfLXKODxUsqyRMiiDCwPg47gj4Kr34qhHDfwYbXsh5TgnXYlvUJJ+nPeC6ry1PSaxFK1So5TbvuRafKppLsZThd8Yt0NquNzBA70NFz/E+fSf9HUyOptCNFQYRRBigLKJFT8jU5yhrQowVdkmx84c+O3dEVFGTfOwMjXl5SmJMzqFCLUVbBJA8X6tuMIqcN2KMMew7xr7TKkYopuuWHRtdXdO1h65D+TiEvywiiDBACWWzvdQqRK+UmdQmlm01b8fv6xCbJVZEVFGT/Ph42JkVLtU2dnLPC2nGtgOXUOuzSGEdmptVKIkJ9xjj8CWz9aEqRyjanmX9etyhfNk253gmEUQY4AgXzXaCIqlCUpuYWRpNk0J2hx4qdHEsfmWr6ENy45iE2OFhWhpzVzpripDMKdSOjOCT2vX3mxefgYHyM1c2A5REXhg/Lqzg7duHyh7P2brkCV3pQzmxQhqXtk8EEQa47clFTlJF5jaxDUxslsYFC/ztk+moHNtzhghdHGdHlL1Y+QhTLiGW2u9tWYipQjK3mQ+b80P3S1MoN3d/a0byFm6fDR/2bCnfQt0YFSmcpO9FEbpGRuhrWqjzrQgiDFDtyXmlyEmqKC9v10LrI8i5FmmXwBNL6AppxypopJSiO9pxhUkDJCHb2XOZfN8Xt8Og7/WKFPLrDkYQ95knsmPI1yeE490VHTXmOzb7+pINH+U7oeHIIogwgY0+iNnRfSgi7j1vocWGP7ommPS9QgUeH6ELI4x2d0/X6FRtsaI42sXWBHIId1wOgz7Xi9XfqqTy5wAriPtu+PQYyjtbyvX90D4Ua7Nh6gscwhbVbCUakf+lbEFEKZwvArXEzikSWyOC2TV3dPi1TXaR5hJ4fIUuijAaWzgKWaywjnbcqfSzk3IMcxfGYZCSU8J1vRhCfhVMeJxQBfGQDR9lcdX3MPn3UJ1OY202TH2hp4fml2UrGzaIj4gXMQURyqSe54tALbGzrMaOe8cutDNm+LeRfid5AyebsdV1PV8oobCxhCOOxQrT52Pk2kj3tzIcgPParozonXTdqmDC48TXL8lHs7FmDf6zaWEjVAMVY7PBZWJy1UWiZjyIJYj4TOqctvPYGhH9jLHi3rl3zaaycSPeobC7O36+h3QCIJfw02jwC0ehixVV6Ob0jco+b9HJobgXeh+fG1vbY+aUzs5kHNTJVOMriPs4YmI/d955vG3IrRnjXF/y+qRL6OMMRxZBxIHvxMSxUyzDNyBG3Du1LXxMWYOD+BDL17wmntDl++xcwlGoCthH6Ob2jcpOykUlh8K0XW9vstBTdsbY+ue1PWUc1cVUw5ljBiPwjY3hovN6e3nnXW6NSAxNpGtMpTdWklk1B25BJGRSx0rAK1cWtyhin5migsR83mfXrPMAbNuWP8F0ddGuPWOGUl/9ql3o4nQExPaD/n5aP7DVsazIHc5wSF3WrZvqfBc7ORR35FZe+6Trj2l7imaxDqYa7jwVeUKNbouY+YrynhWz2cDMP7G0zNhzmGIggoiFkEmd8t0qZuDDQNk9U+2ZaRWla0epBw91wA0N2b3NOR0BY/QDVx19VcAcznS6Pdet450c9bO5QrI5BEefyZ2y4IeGlGNNj5R3ViYUwQ8r7GGuUdTpuNn3ffHF7nc1MoKff2JpRLBtHQMRRCyEdFhO23AV8dk9j4wkCckwbZoV7myLNHZ3ky1r1vA8Ux7c/SCvjr67PV+h21RfzDNrLRZGOM3rU1yCo+/kXpQzd552EPvOTJQx/1C0hXlQBOki8iZRNYQDA7T5BzvGsPMtV18OQQQRC9gOa0snHGrbrqpwErJ7HhvLd960fdfUHr4qyqGh6dd2aVZCBiiXjwPWh8HHuRPbjpdffshktn79dL8cLQRgnpk6WWft9kU7luYV34WLsuHx8cfJ29mXFQ7MKRBQrhXbAdonmkWPW8r8gxljefMtd18OQQQRC5iJKe+8El+zS5VzBYROIHmT6eAgfhLw2cW2tU3P4BlqN86LdjA501LNb9hnxRzrzdGOtgnTJWhkn5lqzhkcPPS9WHkZfB1vfVX51PFEFeBci0rRJ4GnxwnG/wv7Dqna61gO0DGjWUzvEjPGYgivMaiMIHLHHXeoM888Uy1atEgBgLr55ptJ348ZNYN9iTY1GjWPAbeJgBMOG2veZIoVunx2sQMD06+BjbgxPZNLaDT9rbOTJmz5tDtVAB4e5pssqY53lGcDSJ6BazeN9RPiuJerDnn3yy7I4+PJQu7qt3kL+fCwO0KNS02v27i/f/ruXGshQwUCrlwkob55MX03bPMPZoxxCq+xqIwg8s1vflNdccUVauvWraoqgohSyUukOESGDOBYOz1OOBcBmyaCMhFhhcW2tulCCOV5TM/kEhpd75ASCaOham2wQkCsXdy2bXgBnPIOKOdgUIVhk2Ms587dxsCA+zlM/VY/g8+mhSts1oZL+DCNk+z86pu51DXuTCG53Obv2DmTQgQEDuE1JpURRKbcCKoliPioanVkBoUiHKlMZCdeV64EzKDHJFbijNQwTXg9PUliojVrkneRNcdosJNHV9f0XanvAp59tjxTHGbh8J1EYu3ibP4jtveI1UrpsUUdJ+k+rs1XpjY0LeCxVPm6XlSNSLpepk2SKwyT2m+panofjdKCBYn/0bp1/gnZ8jYkRYSmxszvwSUgxOzLIdRWEHn++efVvn37JsuuXbvQD4IldLdI9esoKrQsjY+ZBKuFcD0/h69Jtt5dXUq98520CY3ie+Hzvbxny9vVDg/j++DwcP7zZiki823eRDc+rlR7O/5a+hwMrJaCsjjaJv1YYfa+4yBvg2QzD8c8zMx305Yuvun09f1t2uts/4sRDBDq8EwdN7749OXYwRO1FUTWr1+vAGBa4RREQhebWLZOitrbBWbicO0S8yZ31/OHCF3YCQ8jCGImj6w2hFJ/V8k7WKrRoHm9+zg0x7ZrZ5/HtMhT65AW4PJ2dr6LoylUedu2RMgN2bln8RkHFG2ir88LgPm0aBtcJj79/kyHzeX17+Fh95lVul22bIkXDBDi8Gx7B5TIOuy6QPlsEcETtRVEitCIcCw2FLUaNj6co1NQJg7bM4TYHUNyV1DqjREE8yaPWJEm1N0p1/Oa2pNzF0d9p5Rx1tFxyMyWt7MLWRyzSfWy1+npSbRkoZsBn3FAjaDieGd5c0wRAq2rf1P8XqjXpmLrl8PDhxb/lStx9dqwwf+eHMJCUcETtRVEssTwEeEcXFgVp2unxzmIfJ7N9AyhAgXVCZBab6wgSFVXhi7gFKfLGM+bfXaOXdzcubjPZbVc1HeKVd+HjF+dHwi7mPtO+j7jACu4UfxuMP3KNccUaeIzRRFxOVx3d9v9yajv1dYvuZ2FYwkLRQZPiCDigHO3yHGMO2fSLZ+Jw/QMHCYWiuOU74SnJwOXOtI31JoiNOoyMBB3F0l1aDb1OewBhDokGZuGPETLlS79/XxhwT7Pje2zmLanjIMizWnZ+tjmmKLr5KMhwpbu7qnaC06fCGxfx87nMYWFIoMnKiOIHDhwQO3YsUPt2LFDAYD6zGc+o3bs2KEeffRR1PdjR83YFpc/+RPcy6JG0WQXRd9J3kbZGpF0+1I0Eb6TTn8/LlyTOun4CI36GcfG4plFfByas+0wNmaOprJFVmF39+nr6u+H5DKxaSOKXhxDJn3KOMC0M6c2BDOWizbxpft3DM0ito9RofRJzP1iCgtFBk9URhAZHR1VJufTc889F/X9WIKIUmG7Ra7OzN0pqCGTrtTroXkWqE5WXBOevkZWaKC+pxChkdu5LWTi4SBvd3/RRdMdcHt7/c8NSl/blJulaP8X3fY+wi3VgdDVzmedFe/5bHMMpi93dyv1kY8kP0Pei+7fIyP0M1VCSqgwwnnGDuV6PsJCS2pEQokpiCg1NWeFbycOUd/G6BSUyd+lBi86Np26eFOFxtB6+6Sc5rJxuwS/0BA87Pdtu/vly3mekfLcsQS9vLFSxBENtnbOS5AWWlxzjKlO3d3T5w/f95KNCMJ+f8YMpa68MlxTZIqgo8A9j8cUFjg2mVhEECHA4RTl+/IwBxhRB8n4OC1rLIA5Rfn4OM95KhSw4cMh76qzU6lbbplqhjCZFbL4TA7pRR579orpeV1RBSGLI/X7WaFl8+awd4EtpgmXU9ALGfcxhHKTOS3Ws1L8FkIE1oGB/I0NdS6mznOuks0pRH1fnIt76PXy3lVRm0wRRAgUGUWT7iCDg/hBR+0YvmFvOlOhaTLJO0+FKzlOXhv19YVpsEwl76BDXa+QycG3n2XrkqfFo4Y3+/a58fHi1Oc2FTSHRhNTMHksuJNBpcH2nbPOomkkihKk0hoTl88M9jkpifKwJVQrwr24+14Pu7nwSYBGRQQRApwhaiGHwnFOdKHx99RJK2ZyHNPukDtXB/ZZQyYbX9+Gbdvc7ezTZzA7z7yJuUinUZd/BmeYp6kdKXWMBcfhiKZkYjG1mzZcG5YyQpg53yH34k7dEFJDfrk2jzZEECHAOaGmF400vpkgKYNEd6oNG2iZO6kTc3aBKyo5jr5XUep4l3+C72TjY0PPHnPO0Wewfd6lrqYI8PPm+TmC6/dwxhlmZ9iREZ7xu2aNWfvW2+ufR8WGz+RPNQu6hLaYzrahYB3CY5V168Kfj7u9bCZyk6YUG/Jb1DsVQYQApxe+SRDh2rHF0Lb4lvSEV1RyHA5hLuRZs++UMzQ47/6+fcjWZ3wPBUxDFQDWr+d9L1qgO/NM3v7sEyll6yeYd891ZAFX0i6O+vpStiCiny9WvhEfsBs9yuaiqHcqgggRLlOGaeLn0ri4cnYUvUDr58Q+m01ThIWyEGsHNq424TyMMP08lDT6vn0oVCOi3x2HSWTjxvi+HNSSJyhzCGyaUM0hRpvGuaAUqenUxMrkunx5mF9Jnn9cLCgbvZC2i/VORRAhwiWImCb+0MGVF7pZRuSAfk6KTTekk2MXzqGhZFdoUmVyvlMusD4n1D6E8RHBto9LJUwZN0ND1djxZtvJ1S85TFi6vTk0h3naNK4FJbS+vhrDopPVUYt25qe0Y4hmhWKSC227GE7XIogQiB2+yzG4uDOScj0n9f4+R9orRUsYlH2XvpqRIqIhlMr3ORkfpznnYhcj32Rj2esPD+P9P3p6ksm8DBNbtmD8ejAmEYw2hDMvRF7IP0e/DalviDmnrI0Vtf9jMjeb2mHBAtocSHFS5nIx4Nx4iSBCgEOSdE38oYPrrW+1151blZnuxJjIEGrnnzEjyT1R9DsKfaexnbso4Y55Bes465NvJt0+6cVuy5bw/lVUufBC2jvMM4lg2tonU6atT8RMdhVS33Rb5Y0nFzEi/rJl3ryw7+edlp5nLh8YwL0H7GZBv2uXhhX7bJymaBFECIQu5piJPyQr4tCQ/brUBTq7c812UP0slMgQHx8V7EDUYASevF256+/Zv6WftWiHPQ21XfMOi+O4h20C1NfChhabJvKiis8CTRkPJgGCKjy4+lyIULNhQzKfbNjg7iu+yfu4HNdDjgYoq2gBYHgY17e3bMnvc5h7mqIYTX2VKtRwIIIIAZ/dtim9sY0QjUhbm9sTHutNryeebAZRV0ZRihZgZITuk5E3EE33CJX29THw2QPebO0QssPTDqnr1iVl2zZ3G6bbe9s2fJ8JzQVhy1WAuXd290QxI6WdYItYeBqN5DlNB/thwIwHmwChFydXX+3oSLQ155/v7nM+u2RbX7IJ1Jh5pbNzap/m1NQUYaLp7OTXyjUa+NQJCxbYD5nMc2RP3w8rDBcZ4agRQQQJNnohZAILMStcfHH+9YtK16uxTchUR8R58/IXZ9OzhmRapagdQwbuyIjZ7GFzdvMNv6ae/ux6Vp+wVVM0VIhan2IqcqUNN70r3f7p3xcZZYKta15ZsCDxtbFdJ90vMRov2xyBzXlD1dRgD36LHQ1YNa1Lb6856VzeMyiFF5Jt40uiZnIo+vRdzhekO8eaNf6dE6smKyJdr+0+eiKiOC2avo+FQ/Vtu04a3x0eRqWaft6QCTdGaLFSiYYI8y57eqa/u5CdcVqLtHLl9BTytoPWsn0yW/fYEzBWaN2yhWenr0NRXZsPrFYhT6DGzpGUhR3rK2J6bzrBHIcTetWEEWqxZdLNzql5cww1GgiLCCI5YCd/38WcK8EYdQcf06HSteMLfc7QxSBPlawnH22C6e+3Z+rU+Nrie3ryv9PTg1OX5pVYocUULR7VgZmiAsb26ezn0qa2PDNX0VEm+oiCCy4IHzvZhdrn3Ja8vkTRGnMcP6AUztnT97iMkLB4bOnoiHPdbBkczDcdY+aY3t440YEiiDjAvJis/ZMCp0oxZg6LNHkTfhE2W+pikK3zli1uE9XAgFtIyE5SPs5dlMl/cNDfbBc7tJgyQdsc5oo0F7qoUpSJKbzct+SZjKmLrGvTQ8mngr2fS/DBCI5jY/QTrbMbS+68NrpuRZxKPWOG25Sp64J9xhhrjQgiDmJmA+VasGMuNKYFPE+1V1T4bIgpymZj1b4ElHYfG8NpNrI7Cerk75NptIjF3Od9m0xUVThkzddnRSm8RqbMRFy2McOlEaG2Yai/VswkXukcHiMjuDHuOy5DIiU5C1ZYi2HmFUHEQcxsoJwTUoyUwpQQyyJUmNmyYQPuGVzqyOw5EWNj9HwZ2MiPbEZN6vv3OZwwbzHnMNH5JEcKWchjEuLrgw3b5ggv9y22BYSyKeI6aZkiHNgEn1hJvKhOvBzjcsuWeAeQYgtWEBGNiIMyNSK681KEEewgWrPGro1IlyK8+jEDt6gd35/+ab4vANWs5qN+xToYZxeBsbHpDpZ5pbvb7U9BidjizHlC7S9FmRExmEKhKT4rPmHbHOHlPsXW7tQopDzhFtuGoT5C2LlGh+Lb/CRshRIajyl5aRwofTFG8en/XIgg4sBXisZAMfukO+f69e7Ph2pHQkxGepCFDCDsUeq62BZPikCkr3H55fT6YjUi6UXA10G5v5/Hn4Ijq6Xpmnnq67wxUrRWxPQebAchmtomNGw7JLycUvLq4bvpcLUrtp+G+Aj5aJe6uvBzDNWvRJfs9UMCGTjCuCnvtCyfLRFEcoix28N6l5uySmLUtiHakRCNht71h6gzzzuPPohMA4TqRAmg1Jw59ME7NoabDHVSNmyKc1vfCvWniOmAjQlztJ2f4aOhCRFc8iK7XFEmmlDTQkh4ObW4zES+fdH1HJR+GtKnMSHwpveLKb6CCEAyDjgEalvb+EYDYfpHGT5bIojkoCfXF78Y90LzHHmw8fahHctXeg3x8cju+qmmB4DE94P6PdMuLbaJKN2+2GRQF13kb//v6FDqK19xZ3dN91nb3300RVSoGTp9zRuxDkzLmrmy2XV1e4Y4t+bVzdWf0plVs1qoGTOmf96W+4Fr02F7DxRB0VeopAoiurS15ZsgfCNluE0YtrbJmnJ85ltb/9DXxqb6D0UEEQc+KnSXRgSrKejt9T9kzDQYKIPcZ3KyDbwNG+jX0rk7fJ45u0uLZWM1LXi+Sdq47u/qs+nPUzVFvgKtTfOTvSZmV97dPfX4glDTEkWT4WrPWOG+FPV4emxjckWkCdl0DA0dCoPH3C+G2Y0j8tDVxqFzSNG+UL7zpq1/cPqR5SGCiAVu2ylFJc4Zsz44SOtM1MFnWlj0hEM9kj7U4dV2wienMGLzwSk6LNM2ceQtDNR6+uzuKL4T2PrMm5e0vTaFhdSXksvD1Z6bN7sjHUJ2xlT1uI9AF9pnXYJ32nQ5ODjdDM2xoIXW35SrJdvGvhoXgHjZjGO0R7avxvAjcyGCiAGqpI15OZTdU+wQ2Lz6Uhbw7u5Ddn/T5InREmTrMzxsVjHnFVM+F1/H0GzJC9HmfGfYbIvZQwqxyZ18dnmU3V3Mvq5TllPqm92NX3UVvn1df89biDETtktTEEOT2d09XRsV0xky733ZfIYwhI65tF+Oq41907sXrRHheJ/pgANX35ZD7yxwCiJUyRLjyEOxJxexu87rTLYd2UUXmVOe64O6fOqSbr8QR1dbYrnxcaVuuSXZVfu2V17SOq535ptLAGsf1uYGqqZo3Tr8xFOFvu7yYcgrjUZ4TgfMnMCp+qaa3LLjLXZkhq2kHbmphPQdykLqY2LOu36sCLHQ90kZk5yClggiBiiDesGC6VJ9iDe8Ns3kHe3sozGgdiZbanTfCSf9f9OhZKE2X5sqNEQrgpX+uXaXMcI3TW3k0ybYRZIykcXalW/b5r+TbTTC3kPWBGLrk5yqb2rOo6waPvaxDHnFJzoqpO9QhB+KiVmXs86ibfK480Blr48VrClaSk7TkwgiBqiDOrvDMHWy4eH8ZDGmcF3b/YaH7RMtZWBiOxOHY5hOLGTbAYTujk1CFUbDQskd4SJkN6J3hrG1YbqNMHk/8vp6Xl/Ji0rIs0f7lvZ2pRYv9v9+yNk+tr5oSlblames8Iu9pqmkx6M+YC9m33MVSr6V9KLt23cou3kfjUi2nunnKcL3Iiu8YUyyOmuuaEQCiOEjQnHY7OtT6qtftf+90ThkvjAteJQBi4n59jmIzQXHAtnf776Hr83XNnFTHPiwzoHZyT8b1um7u9y8GV9n36J9SqgZJjFtnYWaGMk33DtGoaYEt10j/Ww+79Tlw2C6JjUZYLpgNkuxS3Yuwi7aPn2HspsPdQLFRojF8L1Ig3G8xUYLhZjUTIggYsHHW9plLtGdzHZwXF64rivJlGmyou5K8+AwGXR3xwkdtu0kqJJ9nt02b0HJ5k/YsAHveDo0FE9DEKNgBFhq5MfYGM03I9bZHGmtka+GK3sNn3qYojpC/bFsJb1ZCr2Wr9k4LRxQo4CofYeymw/ZHPhEiMVych0fx53COz6O6wecGhwRRBz42pjzOll2wYt1/DJ1V+q6Dufz2/BJ2exa2DhtndikZel2pQpWWZVz2XZ7nzYzqYQpTnmYvtZoJG3zzW+GOSCbrms6S4YaCTZrllKf+pRSzz1X7Xdoe35sVJGr+LyX9HEWWDNROgoI23coGzDdn/VGzFcALMv3Ig12Pjr/fNxzcmpwRBBxECOM1tTJYnZQ06mO3CnBQ58/TZ7wlD0xl0PDkifgUdogHSZLTRGdFWSy2Q2/8hX3wXdFFps/DocT3siIfeemnz004V9e22fff9ZpG3PNEIfyopLjmUpIanPfMndumNYhLYy4+g51A+aTjsBU1qzxO5eKk1hpITjqK4KIgxiOgyYnNt8O6mNKmDcvOTgP6wjHPSlhFn1TAiSfsw4wGpbe3vy28OkHvmYDTFh1mYKIrX7cTni2fsAtgPj0rzwVd2j7lvVudSlDEOHskxxzSN44O/NMv7piksD5aBgwaeA//ek47c+hwRFBxAF3aCFG7YvtoKHe5LbzJyj1CpkssPft7Mw/UdglkOXZ+V3toImdYM5UXALbyEh+eHeMYhMqYjrhhUaGmIp2zPTN4xAzsinWCbyUUvQR9FypCNJ+Vtm+Y1ucTe8e25+3bKFHnrmu6etzYVsLuA/GsxXRiKSIffqubVBiMz0CTI92wdrhsh00b/epvd8x18aGl3EMNNcg891RY8wBoeraIhLMZUveLoPzGABbse0oi/JxivEe8oRaDJyC6YIF0yOvyuhv6Xd+yy2J1jTvs1XQ3mRLnikQM19Q8+CcdRa9nhRfNxdlakjFR8RALEFEKfdOHZsy++KLD12P4nOQ7aAYaZ1iFsiqNGNJ0IOD9vb13VFjhZfQHfv4ePGhpRgTVuw6pZ0HXeHJWO3MmjVhWSRDBADt1MiR0ZJTUDCFtGM1sSFpAEJLV1e4eaq7W6m3vIW3Xq6NBXa+oPjshcyZeXmV8ohpIgxpZx9EEEGCUf/nvThqNMUFF0zP0BjTb4V6bcrE59rh+ziVUoQL7PVdE0OR6vL0GTKuCSpWnaiCH7X4ZpEM6fsbNpiFqAULpmb4xQgqnCZbm8CZ57RtUrtTzDqhpj1dr8FBP58SbFg7V/+NMV+Mjob1yVDfihhRndjiq8GxIYIIE3nHwOuQw23bkp0h9oVnfRhiRvJQr93Xh1Ph6kFrwydqiDJZ+LSZr7qWu7gW7RgTka8fCMc98ggRADBJ3Ey7fFv7c4S0+/hMpRcAk9CE7aeXX544L4YIJOkIsTITodlKes6hzBdjY/kmd71ZCHHsxZoqbXmiivYTMx3LwUXlBJF//Md/VMccc4yaNWuWOvnkk9U999yD+l7Zgkjshco3NwWmaBU8dlCtW3cojBHjrJW3w/fRiMQ+WM1m3ilrst282S+ElFps2WS503+bIh0wJhOqVkZvAEJCQ22+VCHPjhXEqKakMvrp6Gj50Vymkt64YOeL/v5izB2uBJXZfmbyaYmtDUlrvLgP5jNRKUFk8+bNaubMmepLX/qSevDBB9UHPvABNX/+fPXkk0/mfrdsQSR2ZIUOMx0b48sx0GjgzrdJf14vHr4Tj2mH6ZMFlupQ5rMQZe8bkmnTVoaGEiGNGu6L7QOUtN+mw9pMeWg4i17EKPlHKFFdjUb4pG0SmjD3b2tTavlyWnZZDmL0U1f5i79QauVK3uRyXH1LU6YDsKtk+3la8LRp8ULfq573XT5msftolkoJIieffLJavXr15P8nJibU4sWL1TXXXJP73bIFkSI6eqhNMrTz6l1caMpjV7SOzSYeIry4omaw7Z6uJ4eJwscmTS2Dg3SBMf2sHOm+80p/v1+0VDrjpU1Q0jtHiikU0zbY93XLLVPrStFqUB1qTUnX6pTVlbO4fERcY6HMJHLDw8VkU8bMBRyRZVQqI4iMjY2ptrY2dfPNN0/5/Xvf+1719re/fdrnn3/+ebVv377JsmvXLvSDxKAIlejGjbyaF8puOS0hhy6cLmdIyu4RI7xwqIyzTmU6YVLI8/t46fvUW9f1xS+mPevwcJw6ZYtL24IND9Qnx154oVKrVycZaAcH+Sd13TbY01h9nBEx2iGM0JHOlVK3BGWh0WB5UTNFRRtR8qNw5VLJK3nnmnGG5FKojCCyZ88eBQDqu9/97pTfDwwMqJNPPnna59evX68AYFopUhAxTQgxVaJlaES0P0i6Y3ItnCZnLexu0LUjTue74FiMTBltsddtb58u8GWFq5gaEerz6zYvIlwZa/LJS+6WfcZYNn5tRsK2DSVviku4zQrW2BxB+jtlJOTzKXoR/OpXafmZsmVggNZfqpBELrTdMJ8bHCwu5w+V2goiZWtEis5mp31EuDQvWHuuaVfHtXD6hq9hwjA56mnbHWCvmw1R7OxMooyyCay487doGzDVqTO2qShb1q4N6ydFOUjqttEbDd9+4+rPeU7fPu8UIKlHaPK72bPjO3Cmw5JD32le24dEG1WtYDcbuk/G1OaFUBlBhGqayVKkjwgms6nu6Fzpkk2ZVYuYhLNpk5XiE4aoO0atAbENtKxKlrITxPqmUK+bV7TanSMcNP0clIUjxFQ0NOTvj0A9YylGunds21CyFVNCk4sQpjjmIB21deGFcerY14dvY0qfwTI2FtcpO0bp6jq0kcGOpbIP3rNRGUFEqcRZdc2aNZP/n5iYUD09PZVyVvXJ0hkqOJiykhbh2KRL2kadFQh8nindRhhTDEUdrXO1UI4SN+0qXPkaONOrpxeuvFw0mNLXR/df6e5O7q3B7g67u6dGkmzbRstt8JGP4J7HltGVu8ydO12A0/2A0iZYISRmJuN00cncQuag7u5E4OQw2dnO+uHUSph29La5psi5lLtQNw8bNtAjFIugUoLI5s2b1axZs9SXv/xl9ZOf/ER98IMfVPPnz1dPPPFE7neLEEQokmdWogxJjW1Tk1Hqc/nlYSfCarUpx7HYLnu36ZyYWDtGjEBkqmNPj5+aHFMPn/wg7e1T87T42LuzwiZmYt6yZWp/pC4kmP64ZUt8rUHaZLZhw6GQ6nQ/oEz06fHpErKLMgcMDYXPQVzFFZHBqWnEzL/alJ7Xt7J/LzO6Jlsvn2yw1AjFIqiUIKKUUp/73OfU0UcfrWbOnKlOPvlkdffdd6O+F1sQoUrNGImcw3EIYybp6irmkDRsWb8ed+5D7B1j3qBz1dH079CiE8u5QlJtRWvNfE082Ukob/E3OQRSFhLs83GbYLJaM1fUie9BaLb5InvNopxItXCktVbr1iVl27bi5gUdSu3SfHIIZi6NtM/1uruVeu65qfP22Fi4VpizpHMlYTUd1AjF2FROEPEl9qF31M6GsbH5JPKy1S+vPrG9wintc/jhbq94/dwxJ8m2tuk7etO7cdXRlAwuxM6c3Z0uWIA/FKyr61Cq7ZB3mDdZZc04aSgLCbY/coaemnZ8rrGd/iw1bw0mN0pRGhFX0rjhYd4Iqfb25N1qIUcn5sIkrOPwPcu+X47NDDVqq+iiN70+uZio+WpiIYJIDj4d2ZSh0gaHmmx8PN85MeYhU7FK7PwHrgkGu0hkT6gt89wNrjTs6XbROTrWrEl+uvo1NmnU5s34uq5cSa+/zWGXepK1/k5eZl2KFi9rDowdjdLba4/20fW+6CKee11+uTk3kKs/ZE01odqL7HzJIezlRZDEcHSdN0+pT30K99m8hItlajqwiCCSg2/iKsoJo6GdBzvYikqaw1ViCyIu3xvsvU3XKDrFti5cGUTTOyxMmDTl2V/72vipwNN5ZDh8NCgTPfXogdiCSGcnLoHVxReH38s3347JL4y6+WtvNwvJHOavPO02VdjB+Jhs2YIT7HVah2y7V0XTgUUEEQchIZVUx5+QzlOXhEXUwhX67JpgQlNj2yapMlS2nBoRzM60p8ds9zc9eywh2OTzgR072JwKaQfUvLFKcWoNfV/64LQtW8IFGt33TckBdVgt1YRMWaBNJpXRUaXe+U7c902RhUqFmXexpnHsO1+zZmriS9vn0v5XeYJ99nT2PEx9V//O5qhdBCKIWOBylDRJrNxQJfKqa0ZM9nZOYURfn+M8Dpufickx0HS/I47gex4Os1D6OtTvdnYeUrXn5X3heo8hXv5YQWD1aryQQwnzDX1+apSTq2gtmCt6jGpCpm6Q0qd0a4fQDRvyfVh0Pg0TvoIIpW9xadZs/leus7Io9bRlIbZdm6LVD0UEEQucjmQ2aR0DRlMS+5yb3l6lzjorzrVtAyudZ4Dz3JB0KDJHe5nCf13Oedn3ibUD5z1PNtrFN78LJWeGraQdFvMyhob2y5CJEqsRodwz9ljUJb34csxVGOd6qgk5pF6UEFnX+8AKwllH8bRQnYdv0AHlOAtq7qrs9W0n+eaVosJ5RRCxwG3u8HmZmBDA9Ge5J79168KEAJ9dX1+fOV9JTw+PMKR3HZxmE0wb2XYuPothtr2y1/QxC82bd8jMUpdD0rZto4+pND4LJWYHWpSPkBYeQuYqrPlBQzEhxxbK8vzoxsfxEUHbtiX9PyuQYIXdmLk5uDQuRfQPX0QQscAdWkd9mdgQQM34eDKQOBwB06YLXylafx/z+bRK1vee2HL55eXlVDEN6pB+Zkq/n+0PmOvMmRNXcxGrhJ6H4WvSwEzONtU75/P394f1IY5FMg/uDVJ3d3K6MsaXgWImy4ss8jV9cESsYAXNbBgvZ1+LnfJdBBELGGm+p4fHsdF2b+xEyOkYmTaN+F4zayrA2jeLSnlddDZJVz/wfea08OYy15X5nEW2Y/q5KU7fIdqLvPGcrUuo9svUB7RZ0EfzQElH74tr/Ic8d/r/Nq0FdgH/yEfy51usQzRHxEr2Glddhe+PscZ97EPwRBBxgFG3USJrsC/TJ10vV4ejnq2RLVkvbu20uXLldG1NdrdQVIKnsku2H4Sq8k0TMbYt58wpvz2oxaaRoJgy877n8x7zwL6TT38ab1JIZ3Kl9p9sNBA3sVPzp/uDSWuBbW+f6KVYjpy+fVH7DMWaQ0UjgiRWHpE8ddv4uFLnncf7MqkHGHF0tHXrpkrwvnbntN2emoeCe8cYs4RMsKZ+EKLVMk3EzRLSjbW5U02ZWdK70FgnlFKcGrFOlmlhiHpooq5/jLwTRWvkTFoLTBRZX59Sa9f63Y/brOVzzpQuWhDhHvfiI0IkZor39EDNS11sKzrmH/NCY0rymAmNUofsoM6G+7kGcNarmzPVNGcxhbj5nHKb1w8oidTyJgzfRHxVKv39OJu7b1SBa7xjMsTmHRFgWtwHBtz11OPCRxiijFnXqcYcu31sXTo64kb72bLGpk3QvqYj30Xa1Dc4Tt4eHY2jEck7I4gDEUQIcPhiYAY5dufEqUHI7u6Gh+mDEuvr0WiYz2mpWrn88ulJf7KJgHyjAmz9IHQi0ea6stuOo5gSzplCFGNoMDBmBduO2La454WMDwzg5xjTIkiZD7RZOdRB0wZ2Z97fX0yEUbaEmqBD+pUplwfHM23cSJ+TXHlEZsxQau7c6f04hklKBBEkXPZO7CDH+KdwSb/a6U1DVatm/UKK9vXQIb/cE1pnp/978u0HoSptTnMdpqxcGcf5t60t/7wm6sZAT9TZRHM6eVZW2MnbpZqEgZB5oqsL911T3xkZwWsUdX6MUC2SS0ik+rkVvSnRicM4TBlYX6HYPjNZf6G8ey1YkLQDxSQUK9JKBBEE3PZOrEoP45/CEaevwwA12ElE557IPkdM/wSXB3uMCQ0rNJp2wOvX5y/SpgMSQzQaWO0A1q8pr+j25zQTpq/tanNqvx8cNO/+spmG9a4POw60f1Xo6cfYkjVPUdpCZ3r2yU2B6fPYuSk7B46NFWua1fcuSiMS02fGNCdiskbrd0PVyMTwGxFBBEGsHX725Fab34DrHACO5EnZgURxljXtimK1F0YaN2UTDGkb16Cz+Q5R28EURkm1GVPNdVpz4mqbGTPwC0mM5FWuQwmpk3pWxYzpZ2eeSbtHEQtpNncMti30e6EmrXMd6mhrt7wsv6ZxXEZuHz1OfXPoUBbk2FrirDDR25vMIdu2xUtXwBlJI4IIglg7fKz9zbb70GnQ+/v9kyWFHFZlS2U+PBwnQZZPciAuLUl20GGc/Cj9JutjMzpK9+bv76f5S+QJsTZzV17kCpcwYpvoWiXM21R8ncrb2/18EbJ+Onlp+7OLMybJ18hIObl9tCbYRwNJNVHEWkPycjTFdFrnzC0iggiCoiY+m+0XO7EvWJAk5+nuxjna2QYSRq1qs2fr63KeTZMXaULRKmHaxlT0yZk60gCzI6T0Gz2Bm1SqWc0I9f+m+6SjOEzf1yeAUrNFcgh+eTvNZglN9im+2kvfd+B7MGQ6HYBrjBaVa8RUtFlUb+ba26d/pqvLfOSE7YA6G1xryJo1ySGMF16Y5JvJEwpjCniiETFQhI8IZcCYOjVlAkhHZVC+22jgHDfztAt5u1vX7oprAOTtOkyLXt5hVaETX09P/rNn3x/XRKvzr6Qnz5D2dLWFSUODDeHL7qApbYDZadZdI2LSMAG4nVVtvlEx2iI7j4RcyxVlUYXsv1lNcleXUu985yFHZt3Xt2zBZ3R1Patve9rO4Cqr/4qPiIUiomYoLyv0+HPfmHDXTqa7255MzIRp8BVZstE42bq5vqtPgDU9axGq4JCMl5jBj5nEs5oOk6Mz9n5ZKMIJxWSDMb/F8EeJXdKLu03D5PKp0OMh/XttBuVui74+/oMhTWOxigIlRStNNc/4mC7nzk0EopAzuDo787Xb1DaSqBkLsQWR8XHaC/PZsabLxo1haldMDgYXHCp21wDAFO3hn34Ho6OJ+Skb6ZB3nezAie0cl7afjozw5QrQKm9s/YeGwsMrMX0jb3doM/FoPydqH81btMsuWY2oFjZ0+PDllyv1nvccOoTR5VOR5wfg8uWh9KsiHM7T/SSWWamzU6lzzw27hjbbcCfLo86rg4OHTMq+z2Jz2k8LUlhfkljnE4kggsQna2HIYA7NkhfiSMS1iz///PBrpDULnCnQY++qswv4//t/vNfHanRs/YB6omde38DsDrlTiduEm/Xr47xTaslmpHT14Wzoa9a05erbNg0oJftvkb4nup+ECju2hdWVvZZSurv9289FdhyY3p0r0Rilffr6EoFqcHD6nEHRkOr2yMvt44sIIkgoAzP9cqkhfVw+Br6ORFx229B0xbps3MgjGJl2LtxRHrb7UPsPZwmNPMk6HXLtDrmEEtOkTo3YymrXXAnyKL4umCMPst/JCnLY96S1Ktk2pebzoN43ZIxgzoKxFVPEXgyTEraERpCY0g6EtrHNFGjzo6OEW3MjgggSSkhrGkouAtMLp0r3oY5EVbPb5u0IqQUThuurBnUN2KLbFePjQVkEenv5doc+ph0MFIE17ZBoy6xqM5NQdqo6vwxGg2V6Z1gB1pUF2GeBKcIPBxNC7mqjInMYhfZ5G9ln4EqKlxamTW1oe+/UKDkuRBBBghmYJp8GikYkJGNiXgfDErpzp/huYCYcbl8O087FNhnkOXhRBiwlJJprN8SZnp5SJ9fukMvxz9a+eXWjCjyhO1Ufp+j0okYNAadEmGEj5zjHn6mfYM2umD5CEdxiOJFTMD23T1K8RmN6RBVGoMEkakxH6cU8+E4EEQKUnQUl7fW8edPzZIRGRaShqMGroBFJtye3SQO7c8G8a6p5AXNNH18Yl+0X85zcqmxbG3M7/qWhmDB8KDLUNC3IUQ+f7O6enn05/Qym/urqx8uXx3vOdD/B+E1g+jVFc00VRDhNFpzRdCEmvbK0l1lEECGCzRRImbSyZ70ohe9ItqgIV10wsf1lRh+k25NLMPJZ5GKoKTHX1JMyNg035qgAF9T7+bYx1+Rowtf5FkuRArp+h6HpuTELhmt+oApBHP0k66hrOlPKBcUnZmQEr4GYPdseCUWFU6i11YFy+rGNWNpLEyKIeMCdKdA08XJMrL4dKYYTJ6aks5em2zpUMAoZONyRHpRr+joa+kJNSU9t45jCQkwhh9o2If00JJup7zi3vVvfpIy+deLafVM012NjNJ8wV34iLKFCrUvrRb1H9uR1TUztpQkRRBjxkXRtJ8mGTqyhHcnmxPmWt/BPTnnPgjmmWjtTms7dCdFixBBEKBTpyU5Ra8dUm/sIC7GFNsri4avF0FEOnBsA23OXldU0GzI6OposqrZQf99+TtFm+vjileGHRzELU/wTTeMttmCfRQQRJig+IbpTAZizJeqOFjKxcnSkorzSXc/iMnPZMsVyCQ9F2Ud96hHDk53S53zaOLawwC20mfJ5uBYsfSaSj4P1jBlKbd4cTzjIjvMyfMHWrXNHJPnMD9j3l9dHKWYaPf5iC7XZ+qQz8NrmpfQzr1yJu49JAxnb1JlFBBEGfBz+8kIAdYfznVhjdSRs9IctOyTlWfJ2KpRDp6iUeW8TnJqZ9E50aGiqmje2BqaI63MIbbbQXUwf9jUnUjYy1JId52XktdHCkK+jJtfu28aGDcXUB6uN6ukxJ8VzmdN8T1hO143iLyYakQxlCSI+g+rTn87viPPmJfZL34k1pmrNN6KE8ixF2ygp9wZIdrBr15ZjrgnBJTTrXVVsDQzH9V2CWajQRp3sTXX3mRfWrKEvItiSdWovUiOS1aT5an20wMxlJs32E6omy1cbMDKCExhsAi7nu8km3YutpbIhgkgA1I6hXx62w8+Z4xcmmq5bTDW4z2KCDSHEtlGMXRJ1ki7DXOMDZnH0DU2mEnL9mCYzjABs8+vC1NNVKBoR7RP1la/Qc/f09CRp8F2+LI0Gj7NqdjENEYBCTr/FvJu8k7U55h4ffxSOI0NsZWCAXi+JmnFQhiBC6Rjpl0dVi4YMtphq8Ji+GKFnqYRAfT8+7Vm0EyxWaMYstKEhliHkRYL5HqKnoeQjybuPDsG9/PJkU5G32GzenH80gvZDoTq1U0ujgT+0Ux+Yh3Fi5jQJhTiyujRemPv6HGUQkiVaXyPGe6amxY/hnyaCSACUjhGSGyObsZVCUY6OvoQm9qHuSjACgO/kjp2cynCCDVmw0nXL2+UvWBDPfwYjTGUXcmq7UjJzuu6D1YboxRQTLZNV04+OxjPnDAz4mXfzxhe34ETV7GI0Xq40/hThx8d30FZ0e3K/50YDH76cPneKGxFEAsB2jKGh6TbsuXNpHSbEBFF2CKqNEJunj2kJKwCE1CvvPRWZJChNyG6KsljqMjDA3+98JmJqu/pO9un7UIRr7EFtbW1JGLtSvAucq16Yow6oY3B4mHYgZkgIasj73bYt/8RaF6EbLNPzjY/TD3TkLDG0zxoRRALw9cPA5MUoshOUReikr9XwpuiPLFQBYGTEr26uTIVlOuBy7KaoJyrbQtN9Ccm/QFGl+ybQ02YtjJCQdnSmaB64Fzjs/TjMu9S6Dw7iI1mw8yM1mpAqTGtzXEhGXFffxR48Gas/xKISgsjf/u3fqqVLl6o5c+aojo4Or2uUHTWDHajUHUERnaAsfNXg+mTJvOgPja8A4POubJkKlSo+SVCashJYYcYEllBhKu84BI1tTHOWjo5E46AUfhxs2FDsO3QdSucT5YStu48Zm1sj4uuIyvl+TOMF67dDLd3d8QIbMFRCELnyyivVZz7zGfWxj32sdoKIUviB6rvLDvERqTK+joFbttDs6SGTj4/2yjaJFZ0kKEuRu2nXe/Gd1EK0FaYx5VpIQxyosaW7O7kPxcRLub7PhsfWj0PNbCFmbE7zENf1su2BmZOoJbuG+MxFvb2HTvV2Pa+uv+1zsfMmVUIQ0dxwww21FESUyh+oITvSopNnFYXPpECJ/tDfDRUAqDsd23WK0Ijk9cMi/AtiPiOXtgKjnQnNM4Gth/YRyRsHWDOFPrMpb3FxlZAdsKkPhoxB7ui/0OuZxlCo0Kd9hWxjl6KdzZ5Fg31eTI6hWNRWEHn++efVvn37JsuuXbvQD+JLyK6AK2qh2aBOCtR2HB3lEQDGx/E7Upt3eezcLlu24HItpMNK3/MepS69FJc/oa2Nb9cXovXhWgio7T02Fr7g2OpgExrS48Ant46v4KkdYznejc55EjIGTde1HfHgW0+MuYlDq4gJkc/ek3J9Ux6gr34VdwaXTesS25m+toLI+vXrFQBMK7EEkdCQS46ohdAcCVmKjKZx3YsyKVDbceNGPgGAelKnqX/Eyu0yMODuPz6hpdly1llhE3C6hPrB2FTjPosEt3+BTxkaMp+6mz5fJC9iwtaPdVth03b7vh9MRtqQMaifw3SwpWsuxiZRxJhjQrWJ1HFOvWd/P05QT4fZ63bYsME9v8X0FYkmiFxyySXKJCiky0MPPTTlO1XViOQNsOx5ACZiRC1wZxaMpXnB3As7KfhoRHQduNWxvpMOd26X4eH8uugJJGRHt2GD31kWRU1mvgIWVjtDPYuEWnp7zZsNzDvDmppiJQrE5ucIFcJ9ot+45jmOOZw6zqn3HBzEjW/dXi6nf1uJ4UwfTRB56qmn1EMPPeQsY9pt/H+poo8IVSK1dXJOR7u8wYfxE6AMZlu7YAQH7rwZVO97X80L5hmw78h0Yi1XRtLxcXyuhZDMjgB405RODY5dcDg1c+lrYeuLmVhHRmins3KNZ2x/xy6uoSYSG9gFE5N91QY1+o177gnRamcz4mIYH6dpsbCh46ElhjN9bU0zWWIJIlSJ1NXJY4QFmgafawfAkcuCKzGY7+4YowEAMNu5y1DHApgnYB91chZK/6RMaqb3hNUIbNhAiySLfW6Mjzkg3f7YXWaM8UyJLMO2iUurRfVf0FCcUX0FT4qvV4y5J0QjQg048NHuFZVjpFYaEQqPPvqo2rFjhxocHFRz585VO3bsUDt27FAHDhxAXyOWIOIjBbs6uc3pav368M6RtwMYHg7fJVJ2GbGiRIrMxxHTL4BDnUzpnz6CSLqO1HYvQjOXh49JrgqRRboNY4R8Y3w50r9fsCDfKbSIMUlpixj1CdFqU4RrqgZWZ92NcRZNtn/UzkeEwrnnnqtMPiSjhF5SFY0IppObohv0yY++O68LL8x3pKR4/K9bRw9BznbUWHkziszHUfTgpi7O2P7Z3a3UVVfR69fdPdWpjSvqJ5a2zATFJFeFXCvpvhtrgTe1Ccb/x9f0zPE+KW0Ra47w1WpjhWsfDawen2VsmriohCDCQWwfEZ/JyZQm2KbmTf+uChMhwPQDzKiTomhE8MVXnYyduC6+GDfZdHVN94XIHnrHEfVT5DvU7ZRnDggxw61ahfvc6tW05465wGd9liiH9FFMz1yLGKUtYvYvX40Z5l1R5pts7hH9DmOsH7EPShVBBIGvFKzNJdhOqxcC7mQ5oWVgIGkHn3MaYkyiRey+svfCvj/X//PazGfyHBnJ38ledFGYqSG7kHBE/ZSdZdZEiNCJNXvlpWk39d3YCzz12X1Mz1xJGbFtEXuOoOQVco3fLNhxsW6dOdw7NKotXdrb3ed3cUJZv2dAi7JiBcBNNwH09OA+32gA9PUB/PrXACtXAuzejfueUgBPPw3w5S8DjI4CbNyY/Ny8Oblmo+H9CEH8/d8nz79oEe7z+nNtbQCf/Wzy72zd9f+vuy75HAWu605MAGzfDrBpU/JzYsJ8r898Jr9OXV3T+0dvL8DgYP53AZI227sX91n9uZtuAnjnO5M+Y6K9HWB4GODMM3F9sL3d/Hulkp/9/UkbrVgB8MgjU/vozp3J77FQ+1IRYNvfxGGH4T73i18A/O535r/Z+q5t/unpAbjqKoCxMXv/xUJ5dqUAdu0CuPPO6X9bsQJgaAigu/vQ7371K4CPfQxg61b/+umxOjaWPLNprN1006E+GGvu0bS1AXz4w8l9qfOyq62x/f1FLwL4q7+aPq6feSb5aRvLFN70pqSdly3zb6coxJWJwigixbvJxGKTzDFHe1N2gWU70HV3+x8Lzp03A3tdahI1m/2bErmQvV8sdTIm5bM+o4jTzyW7m/ONgChSq4UlRCOiQyddz5PnA9bVlZ8HJD3/cEYb+Ty7Kx276fmxPhKmPCrZZ+3pweVvijX3ZJ+Xov10aUQw4yIvTLfR4D0XqYjM3mKaCcDVyWM4uY6NJerAN72Jr5NR6+WrJo6VxdV2XZegQZ0sOc6q4VQnUw6/Gh3l9XNJP2No6G1eu3BnEs4jNNfP+efb3xtAvtpcC47YdsP231jPbhJKQxyQKQ60lGeNNfe46u3z/Onrud5vUWG6HP0Kiwgigdg6eRFhv0UXzmPBY0INT8x7B6GOb+PjyeSR3aXY8mpwatqwKe6xqeuzmWptbYzZrerrmPqSKeNjETuzGLl++vrCE4npeSZmGm5sxJDtHiGaQ59oJa0d4EgMaIIiwOjP9vdPHQfZ8YvNHmuao7TGDLu2dHbma+go/m8xNZQiiEQiRiI0yvW6u5Vau5ZvMs1Okj6DtKgzbTgEtuyz+poRTAttZ2eyMI2N4bU5vpq2rOCQJ+BgnpHaxnkCRLZ/2I5UL2JnZhMafcvgIM08xmWW9Y02yruX6x1QFsj0/3XqAo725hJWQ7R9IRu1vLmeMgfkuQ+MjBwae1hn6xjJzJQSQSQa1Mna1lGp1+HwUbHVz3eXVeTOlssMkV0QfBNjUTQz2Qy4oZo2aop77DNyCtlZMP09e8w5Fzahcf16P5ONr/9Ptk4+2pmQaKP07h5zYqumqFB3rr5mg8PPZdu2ZHFftw6f2h1r2nruObxWDCsUlR3FJoJIRFwnogIkp5lyH/LG4aNi6tg+AzuGLTsPLsdMk+RP2en4aGYw7UJ5r7Z65WU7zXtGbrNjGuxR97pw7oBdfXVgwN9kk84Rg9Wq6cXMVzNTZP6V9Gdj5bGI0ddcz+B77ZCNFyU5IWUOwbzDovP6ZBFBJBKYhQgzWLCT/po14T4qnZ2HDixLd/q89M4+zx/L5hgqgOXVCzsx+9YDc/+8yV6nfPYl7xljOGIrlUye1IWXQ6jF9lVT3gZMSftWYTROIf5gsW35ecTwsYnR12yELMihGy+OTZSvr17ZUWwiiEQCu7PLC+XyPRsmZLEYHDSrZSm7Ty4J27QouhZKzIDiOI48j9BJJW/Bdk32XMmjbITsfNets4dT+y5eoZMkpa+m+57P2MSax3zbIbYPDQbTM5YhmPiYEXxNFBwbr9BNlE6x4EsRifNsiCASAcrOzhXyGRISFrJYzJ1Ll+yzwgH2pFbXZGEL53P5Vujv5Q2o2JE/oZNK3iRaduQSx85Xv7cYDsYUQhcf6i7SJkiHtkOVItd8BDZbG+pxT/3uunV0Ta7vBopj48Vh2go1nZQ1r4ggwgx1R0NR8ZkGqUtSjaEmNU2ups6bPa+EOnAo7WhqB8yAihnNEzqpYCaUIqORTISGlOv3xpUXwdeRjkMdz7GL9BFeYznucoIV9GbPto/ZdF+nnqlCidpav96dKNAmXHI5e4bO2RzOpGXMKyKIMELZ0eRpMjDXwEiqsfKP5OWT8H1+ahu4rleFhZo6qZRt46eSbmNbuGDe83KFyvruBkPt41y7SB9znj4HqspQBCxsEjvK2MqLbKNGJZquw+nsaaoTNc9P3RBBhBHKgAvt0END+MWKS02aLulEWZhnxU4M1Has+kC0mZd82gVDFYSvohPvcQhvoZoNjnb36fd1EFop8wTleSh9zabJpQjNLidwbmfPbH/yPV6jLoggwgh2R+M6UyJ2PPf4OM8OdHTUP9wsb7cY4uhZ5GmtWEyLVAxbbNE5W2yknxebKGnuXPciUoSDcdl+N77mvKLNeD7XGhnhfZ5sXagJuXz9cXycyLn6aJnOpLERQYQR7MK8bVv4NYaG/CeVs87yX+jTkjdWYNA2bGx9m0kj4oJzcSgjZwsGjnDqohyMlaqGRolq3vJxbPYVUEOupdOfhz6PCeoGzrdflu1EXrawHAsRRBjhUM9h80T4TiqUnYntGagZNqnCgc/OsO6qyRDKytlCqZuv812RDsZVgWrewuzSTX2CKqCGXitm0izqtX21rlVwIm/GMSCCCDMc6jPqrohixw613w8OTr9eDLsllzNaK1B2VsQ8fHb5nZ341NhcVGmCHx/Pz6yaN744BVSOa8WcL6jXpmpEWnmjUwQiiEQgT32GmfBM1/AJK0sTqiYHmK6adKWxDxUOsHlEmkE1GULZ50Rg8HFiLVJwqop/jalevhsbTgGV61ox/Rwo16Zo6lp9o1MEIohEwiZsYCY8/d0NGxJfEP0zdCLgSCGczRLpGsgcoYXUzKqtSNU1Ihr93tasqZbgVFX/mnT9fPwCOAVUzmv5Po/vBs52baymznWeVOx5qFXmOhFECgQz4dkEFQ5HrxCNSFbjgjHziCqzGGKqvGNQJcGpyv412XpSF6QqakR8n4eisaJc23bdwUG6wGPbUPoKEVXV0sVABJHIpLUbeacm6hBF09+wAoNrIvB1HDTtDGPkOxH8qVNoX5UEpyoJRdxwtnOZ7yy2xspHKPLdUFKCClz3wCZ+qwsiiESEO7lTW5tbiNCHHrkGVp468swzcXk/KGaeZpXiQ+FWu9YptK8qglMd/GtC4GznMt5Z1TRWmPq4NpRcQQUhkZNVRASRSPimPscU13Wxh8KFOtNSs8hSJqpWsIvGUrvWKXSwCoJTM2tENJztXPQ7q9r74ciLEyOooIqaTwoiiOTgM/FyhMnaSn+/3zksJq/xkAWFaubB7lxawS5adedIGzHeTdlCZ5XMRDEpO7OqL1XTWHE4/OcJTr73qHNfFUHEge/EyxEm6+rAY2P4Q5BidlKf/BBFJV+qKlVTNWNp5nfDaXIoW7BqNqqmESnipOjQ9aOO2jsRRCyETLy+Eq3NtphdoKqUAp3qB2MbgHVdoKlUbWLFUMd3wxGVQTU5tII2r2iqpLEaH1eqp4dHEIkRVIARcqoKZf2eAS3CxATA2rXJa82if9ffn3zOxKJFfvf9yEeSn43G1N/r/193HUBbG8DevX7XBwj7rokVKwAeeQRgaAj3eVvb3HknwO7d9u8pBbBrV/K5OoNtf+73FELd3s3WrQBLlgCceirAu9+d/FyyJPm9Dd2PR0cBNm5Mfu7cmfwee8+VK6e30549ye9d9xbstLUBfPazyb/z5sXY3Hln8j7zaG+fXldNowHQ1wewbJn9+21tAGefbV5/MPiuP3WhZQSR0Il32TKA3l57Z7Rx3HEAN90E0NMz9fdHHAFw1VUAy5cn/w/paDE6aVsbwIc/7H7mvAFYxwXaB2z7V2kyifVuJiYAtm8H2LQp+WkT7CmECARtbQBvfGOyCLzxjfjFLXTjUhdivC8MK1aY58Xe3uT3WGExFGz/ft/7kp++gtPWrQCf+hS5eighpykoQEPjDadphsNBKsR/Ynw8sUVmz5nQat6qHgpXlXTUVaZKqmYsMd5NLMfXMkxIrdB3q2B2Ktv/hvKeQ7LHYkzdZYe9cyM+IgY4z1XAdqr0BIlNmIMVdIrspKEDsKgFmiNqyPf7VcmhgYX73cRyfC1LIKhaZAc3zeyoTIE6DnzmCKwzLCbXU50QQcQAd0bC0dFDKdrzFh/Krq6qh8L5LtJFLdAcWQ9Dd4dVyKFBgevdxNRalCUQNLNGBLND14kUW4HYh/Zh+hFAkqm7maKzRBCxEKPDYRYf6qTWbIfCxV6gQ3d3nLvDur0njncTa9EeH+c5GNKHOprbsGDfV3d3dYVobmLMUdTcU3UUal2IIOIgVodzLT7NrubFEGuBDt2NVzGMtWhhJvR+Mfq3rwmUE9+NS9WFUUoqglYz03C+N0pKhroKtS5EEMmh6ImiCDVv1Se/WIS2bVEqeOz7qYIDIRXuNsQepVCEPwN141KH90c9yqEZF8kioAh8VeofXIggUjFiq3nrMPnFInQ3HktblRY8Bgdx78dlIgLIP8acCpfwyu1/hVVnF+V/QxEi6+AA6hOh12xmgyLACnyDg2XXNA4iiFSQWA5RdZn8YlFFjQjGrEB1aM6WUEGTW3jl6t/Y9zE0VK1dehVNfC6oB3g2s9k4FhiBr7e3On2Cm0oIIjt37lTve9/71JIlS9Ts2bPVS17yEnXllVeqMYIrdjMJIkrx+6cUNflV2ewTuhsvKow179rUFP+hDtYxhFeO/l1Xf6o6RtmMjCi1YEH96l0nmtXPCEMlBJFvfetb6rzzzlO33HKL+sUvfqG+/vWvqyOPPFJddNFF6Gs0myCiFG8HK2Lyq4PZJ3Q3XlQYq+v9+Jxl1Ggk99u2Dd+fYguvof27jgu6UvUVoMbGlGpvd9e5q6u5nbVj04x+RhgqIYiY+OQnP6mOPfZY9OebURDhJPbkVyezT+huvMgwVtP74TrdOW/CqvpCX9ew2SLblXOhHh+fnqOoTEGkWRbhLM3mZ4ShsoLIFVdcoV7zmtdY//7888+rffv2TZZdu3aJIOIg5uRXN5u3UuVmVlXK/4Rmfa+Q0zmxExZFeC1rZ1q3LLVKFSdAcS/UVRJMm2kR9qGOc66LSgoiP//5z1V7e7v6whe+YP3M+vXrFQBMKyKImIk5+VVpgqoLPn4epmMAOIQR23unePKXuTOtW5ZapeILUDEW6qqYlJptEfah2ebcqILIJZdcYhQW0uWhhx6a8p3du3erl770per973+/89qiEaETa/KrygTFQVE7e4pWw/R+xsfNByP6FtOEhRFeu7qqsTOto69ALAEq1kJdlcWvKvUok2aac5WKLIg89dRT6qGHHnKWdGTMnj171HHHHafOOeccNTExEe1BWpkYk1+zTAxF25yxWo3s+zHVs7NTqbPO8teS2CYsl/AK4PYZaIWdaSgxBKiYafSr4JPTbIuwD9h3vG1bPQT0yphmdu/erY477jj1rne9S417tJYIIni4J7+qTFAhlGVztgk/toRkefUcGPCPxqHUsa8Pf1Jo1QXQZiPmQl0Fn5xm2fiEgNVW1sWZtxKCyO7du9XLXvYyddppp6ndu3ervXv3ThYsIoiUSxUmKF/KtjljBUNsPcfGDl1v2zYeIdFUR9mZVhPsQr1und9GpGyfnGbY+HCQp620tU0V5+NKCCI33HCDsvmQYBFBpHzKnqB8qcsOy7eesYTEurSbpo5+JD5Qo6p8dsllt2UdNz4x2symUa2bybQSgggHIohUg7InKB/qsrMPqWfMo8vrsDOtS84JrvFDiaqq8uLtok4bn5j9L9tntm2r1wZBKRFEBKE2O/vQesbakVV9Z1qXnBMxzvTB+gtVSWikUIeNT9H9ry4bqzSU9buhlFJQUfbv3w8dHR2wb98+aG9vL7s6QglMTADceSfA3r0AixYBLFsG0NaG+96SJQB79iRDNEujAdDbC7BzJ+56sahqPbduBVi7FmD37kO/6+sDuO46gBUrwq/v+171d5csmVq3NFV5t1u3AqxcOf29NhrJz5tumt6WmHbRn7ntNoC//dv8eoyOArzxjd6PIWQoo/9t3w5w6qn5n6vSuyat39HFogBEI9LahO4m67CzV4q/nlw7ylg709D3Wgdtl4+zNLVd6rhLbgbK6H91MplqxDQj1B4u1WddbM5c9ay63wTHe63DAkxdrHzapQ4CWTNSVv+ry8ZKI4KIUGu4Q2/rYHNWKryeVfeb4HqvdViAqWf6+LRLHXfJzUCZ/a8uGyulxEdEqDl1tIeWTR38Jrjea1X9atJQnhXAv120HwrA1LZw+aEIYZTd/0L8q4qEsn7PKKhOgoBm717ez7UCd95pF0IAkglz167kc2XB9V7b2gA++9nk33rB1ej/X3dduZPzsmXJYpStn6bRSJx/ly0La5cVKxJho6dn6u97e0UIiUXZ/a+tLRFIzz47+Zl3n4mJRDDetCn5OTERp14hiCAiVI5Fi3g/1wrUQXjjfK9VX4Api1Vou6xYAfDII4nGZOPG5OfOneW3QTNT9f6n2bo10d6ceirAu9+d/FyyJPl9lRDTjFA5ylZ91pE6mLNivNeqq6kxYdDS3+tLlfufT/g4J5T1WwQRoZKI7ZtGXRazVnyvmMWqFduFSpUX/apRBZ8x8RERak9dVJ9VoWy7NZZWfK8Ym34rtguFupgYqkIdfMbSiEakBrTyTqCVn92H2BlRuZD3akbaZTplmxjqyKZNicCWx8aNiYAcAzHNNBGmhaW3N9n9yuATTMhiJjQLVTAx1JEq+IyJINIkyE5AEIRWBrugDg0BLFwogremCj5j4iPSBExMJJoQUyfSv+vvr2ZMuCAIAgfYcPOPflR8R9LUxWdMI4JIRambs5EgCAI3PrmC9uxJNMmtLozUyQH6sLIrIJipQ4IqQSgb8YdpbnSGWpuJwYRSya6/vx9g+fLW7g8rViRtUPUxIoJIRZHsooLgRhy5mx9tYli5MhEuKMKI1hi3+nlUOny8yohppqJQzqoQhFZDO3JnzZeilm8+bCYGDKIxrgciiFSUujkbCUJRiCN365E9T2doCPc90RjXAxFEKkydnI0EoSjEkbs1SWeo/fCHRWPcTIiPSMWpi7ORIBSFOHILLt8R0RjXDxFEakAdnI0EoSjEkVsAOKQxNjksV+1IA8GNZFYVBKFWVCFrpFAdJIS7mlDWb9GICIJQKzBq+U9/WhanVkE0xvVHBBFBEGqHSy3/rncBfOxjkl9EEOqCmGYEQagtWbX8r38N8Fd/JQdFCkLZiGlGEISWIK2W174jtvwikvZbEKqJ5BERBKEpkPwiglBPRBARBKEpkPwiglBPxDQjCEJTgM0b8uSTAJs2STSNRsJfhbIRQUQQhKYAc2R8WxvARz966P+tHk0jJxgLVUBMM4IgNAWugyI12YPwWvm0XjnBWKgKIogIgtA02A6KtJkaWvW0XjnBWKgSIojUiIkJgO3bE/v29u0ySQiCCdOR8a6x0orRNBJhJFQJ8RGpCWLLFQQ86fwimzbhvtNK0TQSYSRUiagakbe//e1w9NFHw+zZs2HRokVwzjnnwOOPPx7zlk2J2HIFwR85rXc60iZClYia4n1oaAiWLl0KixYtgj179sDFF18MAADf/e53Ud+XFO+HskXa1Khy0qgguJHTeqcjbSLEhrJ+R9WIfPSjH4XXve51cMwxx8App5wCl156Kdx9993wwgsvxLxtUyG2XEEIwxVNo/9/3XWtteBKmwhVojBn1WeeeQZuvPFGOOWUU+BFL3qR8TNjY2Owf//+KaXVEVuuIIRji6bp7W3dg/CkTYSqEF0QueSSS+DFL34xdHV1wWOPPQZf//rXrZ+95pproKOjY7L09fXFrl7lEVuuIPCQjaYZHU1MD6284EqbCFWA7CNy6aWXwt/93d85P/PQQw/B8ccfDwAAv/71r+GZZ56BRx99FAYHB6GjowO+8Y1vQMOQcWhsbAzGxsYm/79//37o6+sTH5ElYssVBEEQ6gPFR4QsiPzqV7+Cp59+2vmZl7zkJTBz5sxpv9+9ezf09fXBd7/7XVi6dGnuvcRZNUFHzQBMFUa0LCdqVEEQBKFKUNZvch6R7u5u6O7u9qrYwYMHAQCmaD2EfLQt15RH5LrrRAgRBEEQ6ku08N177rkH7r33XnjDG94ARxxxBPziF7+Aj3/84/Dkk0/Cgw8+CLNmzcq9hmhEpiKnZAqCIAh1IKpGBMvhhx8OW7duhfXr18Nvf/tbWLRoEbzlLW+BdevWoYQQYTrpbJGC0IqIMC4IzUc0QeTEE0+E22+/PdblBUFoMeSYA0FoTuTQO0EQKo8ccyAIzYsIIoIgVBo5sl4QmhsRRARBqDRyzIEgNDciiAiCUGnkmANBaG5EEBEEodLIMQeC0NyIICIIQqVZtiyJjjGcCgEAye/7+pLPCYJQP0QQEQSh0siR9YLQ3IggIghC5ZEj6wWheYmW0EwQBIGTFSsAli+XzKqC0GyIICIIQm2QYw4EofkQ04wgCIIgCKUhgoggCIIgCKUhgoggCIIgCKUhgoggCIIgCKUhgoggCIIgCKUhgoggCIIgCKUhgoggCIIgCKUhgoggCIIgCKUhgoggCIIgCKVR6cyqSikAANi/f3/JNREEQRAEAYtet/U67qLSgsiBAwcAAKCvr6/kmgiCIAiCQOXAgQPQ0dHh/ExDYcSVkjh48CA8/vjjMG/ePGhkz/8OZP/+/dDX1we7du2C9vZ21msLh5B2LgZp5+KQti4GaediiNXOSik4cOAALF68GGbMcHuBVFojMmPGDOjt7Y16j/b2dunkBSDtXAzSzsUhbV0M0s7FEKOd8zQhGnFWFQRBEAShNEQQEQRBEAShNFpWEJk1axasX78eZs2aVXZVmhpp52KQdi4OaetikHYuhiq0c6WdVQVBEARBaG5aViMiCIIgCEL5iCAiCIIgCEJpiCAiCIIgCEJpiCAiCIIgCEJptKQg8k//9E+wZMkSmD17Nrz2ta+F733ve2VXqVZcc8018Md//Mcwb948OPLII+Ev/uIv4OGHH57ymeeffx5Wr14NXV1dMHfuXHjnO98JTz755JTPPPbYY3DGGWfA4YcfDkceeSQMDAzA+Ph4kY9SK6699lpoNBrQ398/+TtpZx727NkD73nPe6CrqwvmzJkDJ554Inz/+9+f/LtSCq688kpYtGgRzJkzB04//XT4+c9/PuUazzzzDKxatQra29th/vz58P73vx9+85vfFP0olWZiYgI+/vGPw7HHHgtz5syBl770pfA3f/M3U84jkbam8+1vfxve9ra3weLFi6HRaMDXvva1KX/natMf//jHsGzZMpg9ezb09fXBJz/5SZ4HUC3G5s2b1cyZM9WXvvQl9eCDD6oPfOADav78+erJJ58su2q14c1vfrO64YYb1AMPPKDuu+8+9ed//ufq6KOPVr/5zW8mP3PBBReovr4+ddttt6nvf//76nWve5065ZRTJv8+Pj6uTjjhBHX66aerHTt2qG9+85tqwYIF6rLLLivjkSrP9773PbVkyRL1qle9Sq1du3by99LO4TzzzDPqmGOOUeedd56655571C9/+Ut1yy23qP/+7/+e/My1116rOjo61Ne+9jX1ox/9SL397W9Xxx57rPrd7343+Zm3vOUt6g//8A/V3Xffre688071spe9TJ199tllPFJlufrqq1VXV5f6xje+oXbu3Km2bNmi5s6dqz772c9Ofkbams43v/lNdcUVV6itW7cqAFA333zzlL9ztOm+ffvUwoUL1apVq9QDDzygNm3apObMmaM+//nPB9e/5QSRk08+Wa1evXry/xMTE2rx4sXqmmuuKbFW9eapp55SAKDuuOMOpZRSzz77rHrRi16ktmzZMvmZhx56SAGAuuuuu5RSycCZMWOGeuKJJyY/c/3116v29nY1NjZW7ANUnAMHDqjjjjtO3XrrrepP//RPJwURaWceLrnkEvWGN7zB+veDBw+qo446Sv393//95O+effZZNWvWLLVp0yallFI/+clPFACoe++9d/Iz3/rWt1Sj0VB79uyJV/maccYZZ6j3ve99U363YsUKtWrVKqWUtDUHWUGEq03/+Z//WR1xxBFT5o1LLrlEvfzlLw+uc0uZZn7/+9/DD37wAzj99NMnfzdjxgw4/fTT4a677iqxZvVm3759AADQ2dkJAAA/+MEP4IUXXpjSzscffzwcffTRk+181113wYknnggLFy6c/Myb3/xm2L9/Pzz44IMF1r76rF69Gs4444wp7Qkg7czFf/zHf8BJJ50Ef/mXfwlHHnkkvPrVr4YvfvGLk3/fuXMnPPHEE1PauaOjA1772tdOaef58+fDSSedNPmZ008/HWbMmAH33HNPcQ9TcU455RS47bbb4Gc/+xkAAPzoRz+C73znO/DWt74VAKStY8DVpnfddRf8yZ/8CcycOXPyM29+85vh4Ycfhv/5n/8JqmOlD73j5te//jVMTExMmZQBABYuXAg//elPS6pVvTl48CD09/fD61//ejjhhBMAAOCJJ56AmTNnwvz586d8duHChfDEE09Mfsb0HvTfhITNmzfDD3/4Q7j33nun/U3amYdf/vKXcP3118PHPvYxuPzyy+Hee++Fj3zkIzBz5kw499xzJ9vJ1I7pdj7yyCOn/P2www6Dzs5OaecUl156Kezfvx+OP/54aGtrg4mJCbj66qth1apVAADS1hHgatMnnngCjj322GnX0H874ogjvOvYUoKIwM/q1avhgQcegO985ztlV6Xp2LVrF6xduxZuvfVWmD17dtnVaVoOHjwIJ510EnziE58AAIBXv/rV8MADD8C//Mu/wLnnnlty7ZqL4eFhuPHGG2Hjxo3wyle+Eu677z7o7++HxYsXS1u3MC1lmlmwYAG0tbVNiyp48skn4aijjiqpVvVlzZo18I1vfANGR0eht7d38vdHHXUU/P73v4dnn312yufT7XzUUUcZ34P+m5CYXp566in4oz/6IzjssMPgsMMOgzvuuAP+4R/+AQ477DBYuHChtDMDixYtgle84hVTfvcHf/AH8NhjjwHAoXZyzRtHHXUUPPXUU1P+Pj4+Ds8884y0c4qBgQG49NJL4V3veheceOKJcM4558BHP/pRuOaaawBA2joGXG0acy5pKUFk5syZ8JrXvAZuu+22yd8dPHgQbrvtNli6dGmJNasXSilYs2YN3HzzzXD77bdPU9e95jWvgRe96EVT2vnhhx+Gxx57bLKdly5dCvfff/+Uzn/rrbdCe3v7tEWhVTnttNPg/vvvh/vuu2+ynHTSSbBq1arJf0s7h/P6179+Wvj5z372MzjmmGMAAODYY4+Fo446ako779+/H+65554p7fzss8/CD37wg8nP3H777XDw4EF47WtfW8BT1IPnnnsOZsyYuuy0tbXBwYMHAUDaOgZcbbp06VL49re/DS+88MLkZ2699VZ4+ctfHmSWAYDWDN+dNWuW+vKXv6x+8pOfqA9+8INq/vz5U6IKBDcf+tCHVEdHh9q+fbvau3fvZHnuuecmP3PBBReoo48+Wt1+++3q+9//vlq6dKlaunTp5N91WOmb3vQmdd9996n/+q//Ut3d3RJWmkM6akYpaWcOvve976nDDjtMXX311ernP/+5uvHGG9Xhhx+uNmzYMPmZa6+9Vs2fP199/etfVz/+8Y/V8uXLjeGPr371q9U999yjvvOd76jjjjuupUNKTZx77rmqp6dnMnx369atasGCBeqv//qvJz8jbU3nwIEDaseOHWrHjh0KANRnPvMZtWPHDvXoo48qpXja9Nlnn1ULFy5U55xzjnrggQfU5s2b1eGHHy7hu7587nOfU0cffbSaOXOmOvnkk9Xdd99ddpVqBQAYyw033DD5md/97nfqwgsvVEcccYQ6/PDD1Tve8Q61d+/eKdd55JFH1Fvf+lY1Z84ctWDBAnXRRRepF154oeCnqRdZQUTamYf//M//VCeccIKaNWuWOv7449UXvvCFKX8/ePCg+vjHP64WLlyoZs2apU477TT18MMPT/nM008/rc4++2w1d+5c1d7ers4//3x14MCBIh+j8uzfv1+tXbtWHX300Wr27NnqJS95ibriiiumhIRKW9MZHR01zsnnnnuuUoqvTX/0ox+pN7zhDWrWrFmqp6dHXXvttSz1byiVSmknCIIgCIJQIC3lIyIIgiAIQrUQQUQQBEEQhNIQQUQQBEEQhNIQQUQQBEEQhNIQQUQQBEEQhNIQQUQQBEEQhNIQQUQQBEEQhNIQQUQQBEEQhNIQQUQQBEEQhNIQQUQQBEEQhNIQQUQQBEEQhNIQQUQQBEEQhNL4/7Czr6GCYSx7AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X[:1000], 'bo')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.021943786501463503"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(X)  # Expected value is about 0. Your values may differ - try a larger sample size!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.stats.api as sms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "results = sms.DescrStatsW(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.014453270331154726, 0.05834084333408173)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.tconfint_mean(0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, 0.0 does sit within the percentage bounds, so we cannot reject the hypothesis that the data has a non-zero mean."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another way to compute this is by taking many samples of the data, computing the mean of each sample, and obtaining the bounds by finding the relevant confidence intervals.\n",
    "\n",
    "Specifically, we need to take a bootstrap sample, which for a dataset of size $n$ is a sample of size $n$ with replacement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "bootstrap_sample = np.random.choice(X, size=len(X), replace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We do this many times (for a large number for \"many\", say 100,000) and compute our statistic of interest for each sample:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "N_ITERATIONS = 100000\n",
    "\n",
    "means = []\n",
    "\n",
    "for i in range(N_ITERATIONS):\n",
    "    bootstrap_sample = np.random.choice(X, size=len(X), replace=True) \n",
    "    means.append(np.mean(bootstrap_sample))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then sort the discovered statistic values, and get the lower and upper bounds, by finding the spot where y% of the values sit within those bounds. For a confidence interval of 95%, we get the 2.5% highest values and the 97.5% highest value for our statistic:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "lower_index = int(0.025 * N_ITERATIONS)   # Hint: try without the call to int\n",
    "upper_index = int(0.975 * N_ITERATIONS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "sorted_means = np.array(sorted(means))\n",
    "lower_bounds = sorted_means[lower_index]\n",
    "upper_bounds = sorted_means[upper_index]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.01434853490028654, 0.058486871505393195)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lower_bounds, upper_bounds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, as zero is within the bounds, we cannot reject the hypothesis that the actual mean of the data is zero. This would be sufficient to continue with our test for white noise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise\n",
    "\n",
    "The constant variance tests in `statsmodels` are not well documented and poorly implemented for directly calling them functions. Instead, use the `scipy` methods for computing constant variance, such as using Bartlett’s and Levene's test. That said, in both cases, these functions don't actually give us the value we are looking for. Instead, they tell whether two datasets have the same variance. A way to use this is to test the first half of the data against the second half.\n",
    "\n",
    "Check the documentation for these two methods, and use the more robust of the two to perform the above test. \n",
    "\n",
    "#### Extended Exercise\n",
    "\n",
    "Note that this test will not work for seasonality issues, like a year's worth of data with a higher summer value.\n",
    "To visually inspect this, we plot the results of the residuals (errors) of our fitted model (such as a linear regression), and visually inspect for patterns. If a clear pattern exists, then we do not have a constant variance (constant variance in error is equivalent).\n",
    "\n",
    "The most useful plot for determining this is residuals on the y-axis, and *fitted values* on the x-axis, i.e what your OLS model predicts for a given input. Create this plot for our `X` data, after generating a random `y` predictor variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1d3258c6250>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = distribution.rvs(1000)  # Random data, between 0 and 1, then with 0.5 subtracted\n",
    "# Note we are considering this as a \"time series\" data, so X[1] happens after X[0]\n",
    "\n",
    "#From solutions\n",
    "from scipy import stats\n",
    "\n",
    "n = int(len(X) / 2)\n",
    "\n",
    "stats.levene(X[:n], X[n:])\n",
    "\n",
    "# Extended exercise solution\n",
    "import statsmodels.api as sm\n",
    "\n",
    "# Create some random \n",
    "y = np.random.random(len(X))\n",
    "est = sm.OLS(y, X).fit()\n",
    "\n",
    "y_pred = est.fittedvalues\n",
    "\n",
    "residuals = y_pred - y\n",
    "\n",
    "plt.plot(y_pred, residuals, 'ro')  # No clear pattern == white noise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*For solutions, see `solutions/residual_plotting.py`*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Checking for autocorrelation\n",
    "\n",
    "We can check the autocorrelation using Panda's `autocorrelate` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x178255c7e88>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.plotting.autocorrelation_plot(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If no statistically significant values are above the confidence lines, then there is no autocorrelation in the data. Occasionally you will see a value appear outside these bounds - if it isn't over by too much, and doesn't happen regularly, this can be a fluke in the dataset. You can check this by doing the same plot on a bootstrapped sample of X - if it still happens, then investigate further for autocorrelation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise\n",
    "\n",
    "Create a dataset with one variable that violates each of the three requirements for white noise. Plot the data to visually see the results. and plot the autocorrelation plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Lag', ylabel='Autocorrelation'>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#From solutions\n",
    "\n",
    "# Mean not 0\n",
    "\n",
    "X = np.random.random(100) + 10  # Mean is about 10.5\n",
    "\n",
    "plt.plot(X)\n",
    "\n",
    "pd.plotting.autocorrelation_plot(X)\n",
    "\n",
    "# Variance not constant\n",
    "\n",
    "i = np.arange(100)\n",
    "X = np.random.random(len(i)) * i\n",
    "\n",
    "plt.plot(X)\n",
    "\n",
    "pd.plotting.autocorrelation_plot(X)\n",
    "\n",
    "# Lagged correlation\n",
    "X = [1] * 100\n",
    "for i in range(1, 100):\n",
    "    X[i] = X[i-1] * np.random.random() * 2\n",
    "    \n",
    "plt.plot(X)\n",
    "\n",
    "pd.plotting.autocorrelation_plot(X)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*For solutions, see `solutions/white_noise_break.py`*"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
